Related papers: Quantized W-algebra of sl(2,1) and quantum parafer…

Starting with its classical parafermion algebra, we consider the quantisation of the SL(2,R)/U(1) WZNW black hole model.

Starting from bosonization, we study the operator that commute or commute up-to a total difference with of any quantized screen operator of a free field. We show that if there exists a operator in the form of a sum of two vertex operators…

Inspired by a result in [Ga], we locate two $ k[q,q^{-1}] $-integer forms of $ F_q[SL(n+1)] $, along with a presentation by generators and relations, and prove that for $ q=1 $ they specialize to $ U({\mathfrak{h}}) $, where $…

The algebra dual to Woronowicz's deformation of the 2-\-di\-men\-sion\-al Euclidean group is constructed. The same algebra is obtained from $SU_{q}(2)$ via contraction on both the group and algebra levels.

We study relations between the two-parameter $\U_q(sl(n))$-invariant deformation quantization on $sl^*(n)$ and the reflection equation algebra. The latter is described by a quantum permutation on $\End(\C^n)$ given explicitly. The…

We define for real $q$ a unital $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ quantizing the universal enveloping $*$-algebra of $\mathfrak{sl}(2,\mathbb{R})$. The $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ is realized as a…

For $\g=sl(n)$ we construct a two parametric $U_h(\g)$-invariant family of algebras, $(S\g)_{t,h}$, which defines a quantization of the function algebra $S\g$ on the coadjoint representation and in the parameter $t$ gives a quantization of…

For a finite dimensional semisimple Lie algebra ${\frak{g}}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\cal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras…

We classify right coideal subalgebras of the finite-dimensional quotient of the quantized enveloping algebra $U_q(\mathfrak{sl}_2)$ and that of the quantized coordinate algebra $\mathcal{O}_q(SL_2)$ at a root of unity $q$ of odd order. All…

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…

We study a W-algebra of central charge 2(k-1)/(k+2) with k a positive integer greater than 1

Using a gauge invariant reduction we directly integrate the SL(2,R)/U(1) WZNW theory. We prove that the conserved parafermions of this theory are coset currents. Quantum mechanically, the parafermion algebra, the energy-momentum tensor, and…

We construct W-algebra generalizations of the ^sl(2) algebra -- W-algebras W^{(2)}_n generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky--Polyakov algebra. We define…

We obtain an explicit expression for the defining relation of the deformed W_N algebra, DWA(^sl_N)_{q,t}. Using this expression we can show that, in the q-->1 limit, DWA(^sl_N)_{q,t} with t=e^{-2\pi i/N}q^{(k+N)/N} reduces to the…

In this article we use a parametrized version of the FRT construction to construct two new coquasitriangular Hopf algebras. The first one, $\widehat{SL_q(2)}$, is a quantization of the coordinate ring on affine $SL(2)$. We show that there…

The deformed $W$-algebra is a quantum deformation of the $W$-algebra ${\cal W}_\beta(\mathfrak{g})$ in conformal field theory. Using the free field construction, we obtain a closed set of quadratic relations of the $W$-currents of the…

We realize the $U_q(\widehat{sl(2)})$ current algebra at arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that the operator product expansions of these parafermionic fields…

We revisit the free field construction of the deformed $W$-superalgebras ${\cal W}_{q,t}(\mathfrak{sl}(2|1))$ by J. Ding and B. Feigin, {\it Contemp.Math.}{\bf 248}, 83-108 (1998), where the basic $W$-current and screening currents have…

We show that the quantum algebra $U_q(sl_2)$ has a presentation with generators $x,x^{-1},y,z$ and relations $x x^{-1}=1$, $x^{-1} x=1$, $\frac{qxy-q^{-1}yx}{q-q^{-1}}=1$, $\frac{qyz-q^{-1}zy}{q-q^{-1}}=1$,…

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…